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ONEMKL RANDOM NUMBER GENERATOR DEVICE ROUTINES



 * Using SYCL* for GPU Offload of Monte Carlo Based Financial Services Workloads
 * The Need for More Flexible Parallel Compute Power
 * RNG Device API Basics
 * American Monte Carlo Options Pricing Model
 * European Monte Carlo Options Pricing Model
 * Use oneMKL RNG Device API Routines to Your Advantage
 * Additional Resources






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Andrey Fedorov 

Math Algorithm Engineer

Gennady Fedorov 

Software Technical Consulting Engineer

Vladimir Polin

AI Software Solutions Engineer

Robert Mueller-Albrecht

Product Marketing Engineer

 

Intel Corporation





By

Andrey Fedorov 

Math Algorithm Engineer

Gennady Fedorov 

Software Technical Consulting Engineer

Vladimir Polin

AI Software Solutions Engineer

Robert Mueller-Albrecht

Product Marketing Engineer

 

Intel Corporation


USING SYCL* FOR GPU OFFLOAD OF MONTE CARLO BASED FINANCIAL SERVICES WORKLOADS


THE NEED FOR MORE FLEXIBLE PARALLEL COMPUTE POWER

The Basel Committee on Banking Supervision* (BCBS) forecasts a four- to
twentyfold increase in compute demand due to the increasing need for financial
risk mitigation measures. These include advanced market prediction algorithms
and risk simulations to understand better asset volatility associated with
climate change, supply chain disruption, and geopolitical changes.

Software developers in the Banking and Financial Services Industry (FSI) rely on
high-performance computing (HPC) environments with GPU-based acceleration to
implement these risk simulation models. The challenge they face is that the wide
deployment of these workloads makes it paramount that they can be run on a large
variety of hardware platform configurations. Before the Unified Acceleration
(UXL) Foundation’s efforts and the ever-increasing popularity of SYCL*, they
faced substantial obstacles and inefficiencies caused by the need to port and
refactor code every time a workload had to be deployed in a new environment.

The Monte Carlo method is a well-known method in finance, relying on highly
performant random number generation as seeds for its simulation scenarios. It is
mainly used for option pricing as the expected return on investment (ROI) is
often too complex to compute directly, especially with exotic options.

American and European Options are two widely used Monte Carlo simulation methods
to predict the probability of various option investment outcomes.

Since the introduction of the C++ with SYCL-based oneAPI Math Kernel Library
(oneMKL) Interfaces in 2020, this component of the oneAPI specification and open
source extension of the Intel® oneAPI Math Kernel Library provides Data Parallel
C++ interfaces for Random Number Generators (RNG) routines implementing commonly
used pseudorandom, quasi-random, and non-deterministic generators with
continuous and discrete distributions.

Just as some other oneMKL function domains, as a part of its implementation,
oneMKL RNG includes:

 1. Manual offload functionality (Random Number Generators Host API)
 2. Device functionality as a set of functions callable directly from SYCL
    kernels (Random Number Generators Device Routines).

We will show how oneMKL Random Number Generators (RNG) Device API helps
you significantly increase the computation performance on Intel® Data Center
GPUs by a factor of 2, compared to the Host API implementation on the same
hardware.

In addition, we will use American Options Pricing using the Monte Carlo
algorithm as an example to demonstrate migrating financial workloads from
proprietary CUDA code to the open, multi-platform SYCL programming model using
SYCLomatic (or the Intel® DPC++ Compatibility Tool).

Results were achieved on Intel® Data Center GPU Max 1550 with the oneAPI 2024.0
release.




RNG DEVICE API BASICS

The main purpose of device interfaces is to make them callable from SYCL
kernels. It brings an essential performance boost because submitting time may
greatly affect the overall execution time of the application.  The idea is to
get random numbers on the fly and process them in the same kernel without paying
for global memory transfer. For example,

Host API:

auto engine = oneapi::mkl::rng::mrg32k3a(*stream, 1ull);
oneapi::mkl::rng::generate(oneapi::mkl::rng::gaussian<double>(0.0, 1.0),
                           engine, n, d_samples);

sycl_queue.parallel_for(
    sycl::nd_range<3>(sycl::range<1>(n_groups) * sycl::range<1>(n_items),
                      sycl::range<1>(n_items)),
    [=](sycl::nd_item<1> item_1) {
        post_processing_kernel(d_samples);
    }).wait();


 

Device API:

sycl_queue.parallel_for(
    sycl::nd_range<3>(sycl::range<1>(n_groups) * sycl::range<1>(n_items),
                      sycl::range<1>(n_items)),
    [=](sycl::nd_item<1> item_1) {
        oneapi::mkl::rng::device::mrg32k3a<1> engine_device(1ull, n);
        oneapi::mkl::rng::device::gaussian<double> distr(0.0, 1.0);
        double rng_val = oneapi::mkl::rng::device::generate(distr, engine_device);

        post_processing_kernel(rng_val);
    }).wait();


 

Since the host interface call takes at least one SYCL kernel, it is easy to see
that the number of kernels required for the implementation when using the Device
API is smaller than the Host API. The RNG Device API is also available as a part
of oneAPI Math Kernel Library (oneMKL) Interfaces, an open-source project that
can be found on GitHub.

Let us consider American and European Monte Carlo workloads separately.


AMERICAN MONTE CARLO OPTIONS PRICING MODEL

To run this benchmark on an Intel® GPU, we took the original code from the
NVIDIA* Developer Code Samples GitHub repository. We then migrated the native
CUDA* GPU code to SYCL using the  SYCLomatic Open-Source Project (SYCLomatic).
This tool is included in the Intel® oneAPI Base Toolkit or available from GitHub
under the Apache* 2.0 license. SYCLomatic allows us to port the original CUDA
code to SYCL and migrates about 95% of the native code automatically to SYCL
code.

Please find step-by-step instructions for the migration of the American Monte
Carlo Options Pricing Model example source code to SYCL, and inspect the SYCL
enabled example source code project in the GitHub repository.

To finish the process, we made some manual code changes and tuned it to the
desired level of performance for our target architecture.

Additionally, after completing the SYCLomatic migration, we added a host
interface call. To reduce the number of SYCL kernels used, we added device calls
to the next kernel (generate_paths_kernel). This way, we reduce the number of
kernels needed and remove the need for extra memory to store random numbers, as
we use these numbers as soon as they are generated.

Applying the Device API interface capability, we obtain up to 2.13 times
performance speed-up compared with traditional host interface calls. We observed
a ~15% performance improvement for the overall application speed-up.

Figure 1 shows the performance scalability of American Monte Carlo benchmark
results depending on the number of calculated paths. The “RNG & Next Kernel
Speedup” curve shows the performance increase of combining RNG device API and
generate_paths_kernel usage compared to the Host API version using RNG Host
interface calls and  generate_paths_kernel separately. “Full Benchmark Workload
Speedup” shows overall the benchmark benefits of using RNG Device API compared
to RNG Host API usage.



Figure 1. American Monte Carlo Scalability Results.

 


EUROPEAN MONTE CARLO OPTIONS PRICING MODEL

Let us also consider the performance of the European Monte Carlo Options Sample
that is available on the oneAPI Samples GitHub. Replacing the Device API with
the Host and modeling for a duration of 1 year, the option_years variable can be
set to 1. After this consideration we can easily replace device calls with a
host call as a separate SYCL kernel. However, we need extra memory to store
generated numbers.

Applying those changes, we found that operating memory on the GPU is
insufficient to store ~100 000 000 000 double precision numbers. So, we decided
to reduce the number of paths to 16000, so we let the code run successfully.



Figure 2 shows how the RNG Device API usage allows users to obtain a 3.69 times
performance improvement for the whole European Monte Carlo benchmark compared to
RNG Host API.


USE ONEMKL RNG DEVICE API ROUTINES TO YOUR ADVANTAGE

Device API allows users to achieve an essential performance boost compared to
Host interfaces but requires much more coding and knowledge about specific
domain implementations. It is also a more flexible API since users can control
the parameters of SYCL parallel routines.

Results in this article can be applied to other applications (not only
financial) that have calculations of random numbers on the critical performance
path.

Addressing challenges is a regular process for Intel® Compiler and Intel® oneMKL
software development teams. To make Intel Software better for our customers. We
are constantly looking for both more efficient algorithms and better
optimization techniques.

To get started now, look at the Intel® oneAPI Math Kernel Library, the oneAPI
Math Kernel Library (oneMKL) Interfaces project, and SYCLomatic.


ADDITIONAL RESOURCES

 * Intel® oneAPI Math Kernel Library
 * oneAPI Math Kernel Library (oneMKL) Interfaces
 * SYCLomatic
 * Intel® DPC++ Compatibility Tool
 * Unified Acceleration (UXL) Foundation

 

Notices & Disclaimers

Performance varies by use, configuration, and other factors. Learn more on the
Performance Index site.

Performance results are based on testing as of dates shown in configurations and
may not reflect all publicly available updates.  See backup for configuration
details.  No product or component can be absolutely secure.

Your costs and results may vary.

Intel technologies may require enabled hardware, software or service activation.

© Intel Corporation.  Intel, the Intel logo, and other Intel marks are
trademarks of Intel Corporation or its subsidiaries.  Other names and brands may
be claimed as the property of others.

*Other names and brands may be claimed as the property of others.




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